Question

rusall From the following data labus Total orders (Q)# of workers (L) # of machines (K) uizzes odules w WN y Media NN edia Gallery urchase Course laterials Which is the correct corresponding production function? anvas to Banner rade Submission O Q=6L+ 5K O Q- 11LK Q = 5L +6K O Q- 7L+4K

Answer 1

Answer

the correct answer is (a) Q = 6L + 5K.

We can see from above table that whenever one additional unit of capital(K) is hired keeping Labor(L) constant then output increases by 5 unit(like Keep L = 1 fixed, then When K = 1, Q = 11 and when K = 2, Q = 16. Thus Output increases by 5 units.)

According to definition of marginal productivity, Marginal productivity of capital is the additional output produced when we increase K by 1 unit. As discussed above when we increase K by 1 unit , Output(Q) increases by 5 units).

Thus Marginal product of Capital(MP_K)= 5 and is constant

Formula:

$MP_K = \frac{\partial Q}{\partial K }$

$=> MP_K = \frac{\partial Q}{\partial K } = 5$

Using above formula :

In option (a) MP_K = 5, In option (b) MP_K = 11L,, In option (c) MP_K = 6 and In option (d) MP_K = 10.

Hence, as we want MP_K = 5 and this is for only option (a). Hence option (a) is the correct answer.

Similarly :

We can see from above table that whenever one additional unit of capital(L) is hired keeping Labor(K) constant then output increases by 6 unit(like Keep K = 3 fixed, then When L = 1, Q = 21 and when L = 2, Q = 27. Thus Output increases by 6 units)

According to definition of marginal productivity, Marginal productivity of Labor is the additional output produced when we increase K by 1 unit. As discussed above when we increase L by 1 unit , Output(Q) increases by 6 units).

Thus Marginal product of Labor(MP_L)= 6

Formula:

$MP_L = \frac{\partial Q}{\partial L }$

$=> MP_L = \frac{\partial Q}{\partial L } = 6$

Using above formula :

In option (a) MP_L = 6, In option (b) MP_L = 11K,, In option (c) MP_L = 5 and In option (d) MP_L = 7.

Hence, as we want MP_L = 5 and this is for only option (a). Hence option (a) is the correct answer.

Hence for both L and K Production function which can describe above data are Q = 6L + 5K.

Hence, the correct answer is (a) Q = 6L + 5K.